I think the two biggest problems here are lack of contrast and.... polish, for lack of a better word. The face and hair look a little flat from lack of strong shadows and highlights, and the line art needs a bit of smoothing. The hair, in particular... it looks like the basic shapes have been blocked in, but not refined.
I did an edit to show you what I mean:

The darker shadows and brighter highlights help give some pop to the image, and help better define the forms. Same with the smoothing or refining, or whatever, of the lines. Most people will tell you that one of the keys of pixel art is exercising control, and careful pixel placement, making sure each dot's in the optimal spot. Like I said, the basic forms are blocked in in yours, they just need a little more love (check the jawline, hair highlights, etc. to see what I mean).

I don't see any reason to drop the 2x outlines. The only thing I'd suggest is that if you're gonna use them, you might want to outline the hair, too. If you were planning on doing that anyway, just pretend I stopped talking at the end of the las bit.
